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  <div class="section" id="norm-unbalance">
<span id="normunbalance"></span><h1><span class="section-number">3.2.4.1. </span>Norm Unbalance<a class="headerlink" href="#norm-unbalance" title="Permalink to this headline">¶</a></h1>
<p>This command is used to construct a convergence test which uses the norm of the right hand side of the matrix equation, i.e. <span class="math notranslate nohighlight">\(b\)</span> vector in <span class="math notranslate nohighlight">\(Ax=b\)</span>, to determine if convergence has been reached. What the right-hand-side of the matrix equation is depends on integrator and constraint handler chosen. Usually, though not always, it is equal to the unbalanced forces in the system. The command to create a NormUnbalance test is the following:</p>
<dl class="function">
<dt>
<code class="sig-name descname">test NormUnbalance $tol $iter &lt;$pFlag&gt; &lt;$nType&gt;</code></dt>
<dd></dd></dl>

<table class="colwidths-given docutils align-default">
<colgroup>
<col style="width: 17%" />
<col style="width: 17%" />
<col style="width: 67%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Argument</p></th>
<th class="head"><p>Type</p></th>
<th class="head"><p>Description</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>$tol</p></td>
<td><p><em>float</em></p></td>
<td><p>the tolerance criteria used to check for convergence</p></td>
</tr>
<tr class="row-odd"><td><p>$iter</p></td>
<td><p><em>integer</em></p></td>
<td><p>the max number of iterations to check before returning failure condition</p></td>
</tr>
<tr class="row-even"><td><p>$pFlag</p></td>
<td><p><em>integer</em></p></td>
<td><blockquote>
<div><div class="line-block">
<div class="line">print flag (optional: default is 0) valid options:</div>
<div class="line">0 print nothing</div>
<div class="line">1 print information on norms each time test() is invoked</div>
<div class="line">2 print information on norms and number of iterations at end of successful test</div>
<div class="line">4 at each step it will print the norms and also the &lt;math&gt;Delta U&lt;/math&gt; and &lt;math&gt;R(U)&lt;/math&gt; vectors.</div>
<div class="line">5 if it fails to converge at end of $numIter it will print an error message BUT RETURN A SUCEESSFULL test.</div>
</div>
</div></blockquote>
</td>
</tr>
<tr class="row-odd"><td><p>$nType</p></td>
<td><p><em>integer</em></p></td>
<td><p>type of norm (optional: default is 2 (0 = max-norm 1 = 1-norm 2 = 2-norm …))</p></td>
</tr>
</tbody>
</table>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>When using a <span class="xref std std-ref">penalty</span> constraint handler, large forces (those necessary to enforce the constraint) are included in the <span class="math notranslate nohighlight">\(b\)</span> vector. Even for very small changes in the displacement, if user has selected overly large penalty factor, large forces can appear in the <span class="math notranslate nohighlight">\(b\)</span> vector.</p>
</div>
<div class="admonition-example admonition">
<p class="admonition-title">Example:</p>
<p>The following examples demonstrate the command to create a NormUnbalance test whcih allows 10 iterations till failure with a 2-norm in the <span class="math notranslate nohighlight">\(b\)</span> vector, i.e. <span class="math notranslate nohighlight">\(\sqrt(b^T b)\)</span> of <strong>1.0e-2</strong>.</p>
<ol class="arabic simple">
<li><p><strong>Tcl Code</strong></p></li>
</ol>
<div class="highlight-tcl notranslate"><div class="highlight"><pre><span></span><span class="nv">test</span> NormUnbalance <span class="mf">1.0</span>e-2  <span class="mi">10</span> <span class="mi">2</span>
</pre></div>
</div>
<ol class="arabic simple" start="2">
<li><p><strong>Python Code</strong></p></li>
</ol>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">test</span><span class="p">(</span><span class="s1">&#39;NormUnbalance&#39;</span><span class="p">,</span> <span class="mf">1.0e-2</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>Code Developed by: <strong>fmk</strong></p>
</div>


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